3 Suspended masses A system of masses and springs is shown in the adjacent figure, for which ki = 6 N m', k2- 15 N m', and ks - 78 N m'. Assume that the blocks move vertically with no rotation or side-to-side swinging. a) Show that the normal mode angular frequencies are 2 rad s' and 3 rad s', and find the corresponding normal modes. ki 4 kg k2 The blocks are held in their equilibrium positions; the 4 kg block is then displaced 1 cm upwards and the system is released from rest. b) Find expressions for the subsequent displacements of both blocks. 12 kg ooo0000000

3 Suspended masses A system of masses and springs is shown in the adjacent figure, for which ki = 6 N m', k2- 15 N m', and ks - 78 N m'. Assume that the blocks move vertically with no rotation or side-to-side swinging. a) Show that the normal mode angular frequencies are 2 rad s' and 3 rad s', and find the corresponding normal modes. ki 4 kg k2 The blocks are held in their equilibrium positions; the 4 kg block is then displaced 1 cm upwards and the system is released from rest. b) Find expressions for the subsequent displacements of both blocks. 12 kg ooo0000000